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NBER WORKING PAPER SERIES SELF-VALIDATING OPTIMUM CURRENCY AREAS Giancarlo Corsetti Paolo Pesenti Working Paper 8783 http://www.nber.org/papers/w8783 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 February 2002 We thank Luca Dedola, Rudi Dornbusch, Petra Geraats, Ken Rogoff, Cedric Tille and seminar participants at the 2002 AEA Meetings in Atlanta for many helpful comments. We also thank Raymond Guiteras for excellent research assistance. Corsetti's work on this paper is part of a research network on `The Analysis of International Capital Markets: Understanding Europe's Role in the Global Economy', funded by the European Commission under the Research Training Network Programme (Contract No. HPRN-CT-199900067). The views expressed herein are those of the authors and not necessarily those of the National Bureau of Economic Research, the International Monetary Fund, the Federal Reserve Bank of New York, the Federal Reserve System, or any other institution with which the authors are affiliated. © 2002 by Giancarlo Corsetti and Paolo Pesenti. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Self-Validating Optimum Currency Areas Giancarlo Corsetti and Paolo Pesenti NBER Working Paper No. 8783 February 2002 JEL No. E5, F4 ABSTRACT In this paper we show that a currency area can be a self-validating optimal policy regime, even when monetary unification does not foster real economic integration and intra-industry trade. In our model exporters choose the degree of exchange rate pass-through onto export prices given monetary policy rules, and monetary authorities choose optimal policy rules taking firms' pass-through as given. We show that there exist two equilibria, which define two self-validating currency regimes. In the first, firms preset prices in domestic currency only, and let foreign-currency prices to be determined by the law of one price. Optimal policy rules then target the domestic output gap and floating exchange rates support the flex-price allocation. In the second equilibrium firms optimally preset prices in local currency, and a monetary union is the optimal policy choice for all countries. Although business cycles are more synchronized with a common currency, flexible exchange rates are superior in terms of welfare. Giancarlo Corsetti Department of Economics University of Rome III Via Ostiense 139 00154 Rome, Italy [email protected] Paolo Pesenti Research Department International Monetary Fund 700 19th Street, NW Washington, DC 20431 and NBER Tel: 202-623-4256 Fax: 202-623-6334 [email protected] 1 Introduction In the vast literature on optimum currency areas (OCAs), an influential contribution by Frankel and Rose [1997, 1998] suggests that a monetary union may become optimal ex-post, even though the individual countries that join it do not meet the optimality criteria ex-ante. The argument is that the elimination of foreign exchange transaction costs has real effects and foster economic integration. To the extent that economic integration enhances intra-industry trade rather than product specialization, national business cycles become more synchronized, since sectoral demand shocks and productivity innovations affect all countries at the same time. Higher national output correlation then reduces the need for exchange rate adjustments to stabilize national employment and prices, and minimizes the welfare costs of giving up national currencies. Using thirty years of data for twenty industrialized countries, Frankel and Rose [1997, 1998] provide empirical evidence that countries with closer trade links exhibit more tightly correlated business cycles. Rose and Engel [2000] show that membership in a common currency area increases international business cycle correlations by a significant amount. In this paper, we offer a distinct argument for a theory of endogenous optimal currency areas, with conceptual roots in the Lucas critique. We show that — independent of economic integration — the adoption of a common monetary policy can be self-validating: when the private sector chooses pricing strategies that are optimal in a monetary union, such strategies make a currency area the optimal monetary regime from the vantage point of the national policymakers as well. In other words, there is no incentive for monetary authorities to pursue independent strategies of national output stabilization. As a result, even if there is no structural change in fundamentals (e.g., no increase in intra-industry trade), national outputs become more correlated. In this paper we analyze endogenous optimal monetary unions within a general-equilibrium two-country, choice-theoretic stochastic setting where national welfare is measured by the utility of each country’s representative household.1 The key elements of our approach are imperfect competition in production, nominal rigidities in the goods markets, and forward-looking 1 Other contributions in the recent literature include Obstfeld and Rogoff [2000a, b], Devereux and Engel [2000], Corsetti and Pesenti [2001a], Benigno [2001], Clarida, Gali and Gertler [2001], Canzoneri, Cumby and Diba [2001]. On the welfare effects of a currency area when political factors influence monetary policy see Neumeyer [1998]. 1 price-setting by firms. Drawing on our previous work (Corsetti and Pesenti [2001a]), our setup allows for imperfect pass-through of exchange rate onto export prices. In what follows, the degree of pass-through is endogenously chosen ex-ante by exporters, in the form of a rule of limited price flexibility contingent on exchange rate movements. To distinguish our theory from the previous argument for endogenous optimal currency areas, we rule out a priori structural change: countries are perfectly specialized in the production of one type of good before and after the monetary union. Firms optimally choose prices and pass-through elasticities based on information on shocks and policy rules. Taking firms’ pricing and pass-through strategies as given, monetary authorities choose optimal statecontingent monetary policy rules. In a world equilibrium, both the degree of pass-through and monetary policy are jointly determined by optimizing agents. We show that there are two equilibria, which can be Pareto ranked. While exporters could in principle choose any intermediate level of pass-through, in equilibrium pass-through is either 100 percent or zero as producers optimally choose ‘corner’ pricing strategies to prevent their markups from being affected by exchange rate fluctuations.2 There is one equilibrium in which firms choose to preset prices in domestic currency, and let the foreign price adjust according to the law of one price. With complete pass-through, monetary policies are fully inward-looking: they implement stabilization rules that close national output gaps completely in every period. This equilibrium is inconsistent with fixed exchange rates, and implies low correlation among output levels — depending on the cross-country correlation of fundamental shocks. The exchange rate plays the role stressed by Friedman [1953]: it brings about the required relative price adjustments that are hindered by the presence of nominal price rigidities. But there is another equilibrium in which firms preset prices in consumer currency. With zero pass-through in the world economy, monetary policies are perfectly symmetric across countries, that is, they both respond to the same average of national shocks. This equilibrium is consistent with an OCA: there is no cost in giving up monetary sovereignty because, even if 2 Related literature focuses on the choice of pricing strategies where monetary authorities are assumed to implement non-optimizing, noisy policies (as in the work by Bacchetta and Van Wincoop [2001] and Devereux and Engel [2001]) rather than optimal rules. 2 national monetary authorities remained independent, they would still choose to implement the same monetary rules, moving interest rates in tandem and responding symmetrically to world-wide shocks. National outputs are perfectly correlated even when shocks are asymmetric. In welfare terms, the optimal monetary union is Pareto-inferior to the Friedman-style arrangement in the first equilibrium. Although the private and the public sector ‘do the right thing’ — in terms of policy and pricing strategies — once the equilibrium with a monetary union is selected, there is still room for welfare improvement by creating conditions for relative price adjustment via changes of the exchange rate. A move toward more volatile rates and less synchronized business cycles would bring about the appropriate change in firms’ pricing and pass-through strategies, which in turn would validate the floating regime as optimal. This paper is organized as follows. Section 2 develops the model. Section 3 studies price-setters’ optimal behavior and endogenous pass-through strategies for given monetary policies. Section 4 focuses instead on optimal monetary policies given firms’ pricing strategies. The previous two pieces of analysis are brought together in sections 5 and 6, which characterize the equilibrium of the economy. A final section discusses our main results. 2 2.1 The model Preferences, technology and budget constraints Following Corsetti and Pesenti [2001a] we model a world economy with two countries, H (Home) and F (Foreign), each specialized in one type of traded good. Each good is produced in a number of brands defined over a continuum of unit mass. Brands are indexed by h in the Home country and f in the Foreign country. Each country is populated by households defined over a continuum of unit mass. Households are indexed by j in the Home country and j ∗ in the Foreign country. Home agent j’s lifetime expected utility W is defined as: Wt−1 (j) ≡ Et−1 ∞ X β τ −t [ln Cτ (j) − κ`τ (j)] 0 < β < 1, κ > 0 (1) τ =t where β is the discount rate. The instantaneous utility is a positive function 3 of the consumption index C(j) and a negative function of labor effort `(j). Foreign agents’ preferences are similarly defined: the discount rate is the same as in the Home country, while κ∗ in the Foreign country need not coincide with κ in the Home country. For each agent j in the Home country, the consumption indexes of Home and Foreign brands are defined as: CH,t (j) ≡ 1 ´Z Ct (h, j) θ−1 θ θ ´Z µ θ−1 , CF,t (j) ≡ dh 1 Ct (f, j) θ ∗ −1 θ∗ df ∗ µ θ∗θ−1 θ, θ∗ > 1. 0 0 (2) where Ct (h, j) and Ct (f, j) are respectively consumption of Home brand h and Foreign brand f by Home agent j at time t. Each Home brand is an imperfect substitute for all other Home brands, with constant elasticity of substitution θ. Similarly the elasticity of substitution among Foreign brands ∗ ∗ is θ∗ . The consumption indexes in the Foreign country, CH,t (j ∗ ) and CF,t (j ∗ ), are analogously defined. We assume that the elasticity of substitution between Home and Foreign types is one, thus smaller than the elasticity of substitution between brands of the same type of good produced in each country, θ and θ∗ . Under this assumption the consumption baskets of individuals j and j ∗ can be written as a Cobb-Douglas function of the Home and Foreign consumption indexes: ∗ ∗ (j ∗ )1−γ (j ∗ )γ CF,t Ct (j) ≡ CH,t (j)γ CF,t (j)1−γ , Ct∗ (j ∗ ) ≡ CH,t 0 < γ < 1 (3) where the weights γ and 1 − γ are identical across countries. We denote the prices of brands h and f in the Home market (thus expressed in the Home currency) as p(h) and p(f ), and the prices in the Foreign market (in Foreign currency) as p∗ (h) and p∗ (f ). Given the prices of brands, we can derive the utility-based price indexes PH , PF , P and their Foreign analogs.3 In particular, the utility-based CPIs are: ∗ ¡γ ∗ ¡1−γ γ PH,t PF1−γ PH,t PF,t ,t ∗ , Pt = γW ≡ γ γ (1 − γ)1−γ . (4) Pt = γW γW 3 For instance, the utility-based price index PH,t is defined as the minimum expenditure required to buy one unit of the composite good CH,t and is derived as PH,t = 1 i 1−θ hR 1 1−θ p (h) dh . t 0 4 Each brand h is produced by a single Home agent and sold in both countries under conditions of monopolistic competition. Output is denoted Y . Technology is linear in household’s h labor, `(h). The resource constraint for brand h is: Z 1 Z 1 `t (h) (5) ≥ Ct (h, j)dj + Ct∗ (h, j ∗ )dj ∗ Yt (h) = αt 0 0 where α is a country-specific productivity shock. The resource constraint for Foreign brand f is similarly defined as a function of the productivity shock in the Foreign country, α∗ . Home agent j receives a revenue R(j) from the sale of the good she produces. Since each agent is the sole producer of a specific brand, we associate individual j with brand h. The sales revenue of agent j, expressed in Home currency, is: Z 1 Z 1 ∗ Ct (h, j ∗ )dj ∗ (6) Rt (j) ≡ pt (h) Ct (h, j)dj + Et pt (h) 0 0 where E is the nominal exchange rate, defined as Home currency per unit of Foreign currency. Home agents hold two international bonds, BH and BF , denominated in Home and Foreign currency, respectively.4 Both international bonds are in zero net supply. The individual flow budget constraint for agent j in the Home country is: BH,t+1 (j) + Et BF,t+1 (j) ≤ (1 + it )BH,t (j) + (1 + i∗t )Et BF,t (j) Z 1 Z 1 +Rt (j) − pt (h)Ct (h, j)dh − pt (f )Ct (f, j)df 0 (7) 0 In the expression above the short-term nominal rates it and i∗t are paid at the beginning of period t and are known at time t − 1. The two short-term rates are directly controlled by the national governments.5 Similar expressions hold for the Foreign country, after associating household j ∗ with brand f . 4 We adopt the notation of Obstfeld and Rogoff [1996, ch.10]. Specifically, our timing convention has BH,t (j) and BF,t (j) as agent j’s nominal bonds accumulated during period t − 1 and carried over into period t. 5 The adoption of a cash-less economy framework is merely motivated in terms of analytical convenience. All the results of this model go through when money demand is 5 Taking prices as given, Home agent j maximizes (1) subject to (7) with respect to consumption and asset holdings. A similar optimization problem is solved by Foreign agent j ∗ . In our analysis below we focus on symmetric equilibria in which at some initial point in time t = 0 all agents have zero net financial wealth. As shown in Corsetti and Pesenti [2001a, b], in equilibrium wealth is zero at any subsequent point in time: Home imports from Foreign are always equal in value to Foreign imports from Home. Since agents are equal within countries (though not necessarily symmetric across countries) we can drop the indexes j and j ∗ and interpret all variables in per-capita (or aggregate) terms. As trade and the current account are always balanced, countries consume precisely their aggregate sales revenue: Rt∗ − Pt∗ Ct∗ = 0. Rt − Pt Ct = 0, 2.2 (8) Nominal rigidities, exchange rate pass-through and price setting It is assumed that individual firms set the nominal price of their product one period in advance, and stand ready to meet demand at given prices for one period. In terms of our notation, Home firms selling in the Home market choose pt (h) at time t − 1 by maximizing (1) subject to (7) with respect to pt (h), accounting for (5) and (6).6 As shown in Corsetti and Pesenti [2001a], explicitly considered. Liquidity demand could easily be introduced in the model through a cash-in-advance constraint of the type Mt (j) = Pt Ct (j) and Mt∗ (j) = Pt∗ Ct∗ (j ∗ ), or through a money-in-utility-function framework. In both cases money demand would be residually determined in equilibrium as a function of nominal interest rates. 6 Standard intratemporal optimization yields agent j’s demand for brand h as a function of the relative price of h and total consumption of Home goods: −θ Ct (h, j) = (pt (h)/PH,t ) CH,t (j) Similar expressions can be derived for the other brands. Accounting for the demand functions above, we can rewrite the resource constraint for agents h in the Home country as: ∗ ¡θ ∗ θ `(h)/αt ≥ pt (h)−θ PH,t CH,t + p∗t (h)−θ PH,t CH,t and sales revenue as: ∗ ¡θ ∗ θ Rt (j) = pt (h)1−θ PH,t CH,t + Et p∗t (h)1−θ PH,t CH,t 6 in an environment in which national agents are symmetric (i.e. all prices pt (h) are equal and pt (h) = PH,t ), Home firms optimally set domestic prices equal to expected nominal marginal cost M Ct (equal to καt Pt Ct in our model), augmented by the equilibrium markup θ/ (θ − 1): pt (h) = PH,t = θ θ Et−1 [καt Pt Ct ] = Et−1 [M Ct ] θ−1 θ−1 (9) Home firms selling abroad also set nominal prices one period in advance. Different from most models in the literature, however, we do not impose a priori the restriction that export prices are set in Home currency, implying that all unexpected fluctuations in the exchange rate are ‘passed through’ one-to-one onto export prices in Foreign currency (in the literature this scenario is referred to as ‘Producer Currency Pricing’ or PCP). At the same time, we do not impose a priori the opposite restriction that export prices are set in Foreign currency, implying that Foreign-currency prices of Home goods do not respond at all to unexpected exchange rate fluctuations (i.e. the case of ‘Local Currency Pricing’ or LCP). We consider instead the more general case in which Home firms preset export prices in Foreign currency but are able to modify them after observing exchange rate changes. In our setup, the extent to which Foreign-currency prices of Home exports adjust contingent on the realization of the exchange rate is a choice variable, determined by Home firms at time t − 1. In other words, the elasticity of exchange rate pass-through can endogenously be zero (as in the LCP case), one (as in the PCP case), or any intermediate number. Formally, Foreign-currency prices of Home brands are modelled as: p∗t (h) ≡ p̃t (h) 0 ≤ ηt∗ ≤ 1 η∗ Et t (10) where p̃t (h) is the predetermined component of the Foreign currency price of good h that cannot be adjusted to variations of the exchange rate during period t and ηt∗ indexes the degree of pass-through in the Foreign market.7 Home firms choose p̃t (h) and ηt∗ one period in advance at time t − 1 in order to maximize (1), while the actual p∗t (h) depends on the realization of the 7 For instance, if η ∗ = 1, pass-through in the Foreign country is complete — as in the PCP case. If η ∗ = 0, we have p∗t (h) = p̃t (h) which coincides with the price chosen by the Home producer in the LCP case. 7 exchange rate at time t. Clearly, depending on firms’ choice, the degree of pass-through may vary over time.8 In equilibrium, we obtain: ∗ = p∗t (h) = PH,t p̃t (h) η∗ Et t = θ θ−1 i h η∗ Et−1 καt Pt∗ Ct∗ Et t η∗ Et t = θ θ−1 h i 1−η ∗ Et−1 M Ct /Et t η∗ Et t (11) Interpreting (11), domestic firms set p̃t (h) such that at the margin the expected disutility from an increase in labor effort is equal to the expected utility from consumption financed by additional sales revenue. Analogous expressions can be derived for the prices set by Foreign firms in the Foreign and the Home market. Define the function: pt (f ) = p̃∗t (f )Etηt , 0 ≤ ηt ≤ 1. (12) The degree of pass-through in the Home country, ηt , need not be equal to that in the Foreign country, ηt∗ . The optimal pricing strategy is such that: ∗ = PF,t θ∗ Et−1 [M Ct∗ ] , θ∗ − 1 PF,t = £ ¢ θ∗ ηt ∗ 1−ηt E M C E E t−1 t t t θ∗ − 1 (13) Clearly, Home firms are willing to supply goods at given prices as long as their ex-post markup does not fall below one: ∗ ≥ PH,t PH,t ≥ M Ct , M Ct Et (14) Otherwise, agents would be better off by not accommodating shocks to demand. In what follows, we restrict the set of shocks so that the ‘participation constraint’ (14) and its Foreign analog are never violated. 8 The model could be easily extended to encompass the case in which the pass-through elasticity is a non-linear function of the exchange rate (e.g., η ∗ is close to zero for small changes of the exchange rate E but close to one for large exchange rate fluctuations). 8 2.3 Monetary policy and the closed-form solution of the model Before deriving the general solution of the model, it is helpful to introduce an index of monetary stance µt such that: ² ³ 1 1 (15) = β(1 + it+1 )Et µt µt+1 or, integrating forward, N −1 1 1 Y N = Et lim β (1 + it+τ +1 ) N →∞ µt µt+N τ =0 (16) This expression shows that the index of monetary stance is a function of both current and future expected Home nominal interest rates: Home monetary easing at time t (a higher µt ) reflects either an interest rate cut at time t (i.e., a lower it+1 ) or expectations of future interest rates cuts. A similar expression holds for the Foreign country. Note that in equilibrium µt is equal to Pt Ct 9 (and µ∗t is equal to Pt∗ Ct∗ ): a monetary expansion delivers increased nominal spending. A monetary union in our framework is defined as a regime in which it+1 = i∗t+1 for all t. If both countries adopt the same numeraire, this implies µt = µ∗t . Table 1 presents the general solution of the model, in which all endogenous variables (17) through (26) are expressed in closed form as functions of real shocks (αt and αt∗ ) and monetary stances (µt and µ∗t ).10 Interpreting Table 1: since the equilibrium current account is always balanced (see (8) above) and the demand for imports is proportional to nominal expenditures Pt Ct and Pt∗ Ct∗ , the nominal exchange rate Et in (17) is proportional to Pt Ct /Pt∗ Ct∗ , that is, a function of the relative monetary stance.11 The relations (18) link marginal costs to macroeconomic shocks and monetary policy. Domestic prices of domestic goods are predetermined according 9 This result can be obtained by comparing the Home Euler equation with logarithmic utility, 1 = β (1 + it+1 ) Et (Pt Ct /Pt+1 Ct+1 ), with (15). 10 Algebraic details can be found in the Appendix of Corsetti and Pesenti [2001a]. Note that the solution does not hinge upon any specific assumption or restriction on the nature of the shocks besides the participation constraints (14) and their Foreign analogs. 11 Note that the exchange rate is a forward-looking variable, as it depends on current and expected future changes in short-term nominal interest rates in the world economy. 9 Table 1: The closed-form solution of the model 1 − γ µt γ µ∗t M Ct = καt µt M Ct∗ = κ∗ αt∗ µ∗t θ PH,t = Et−1 (M Ct ) θ−1 £ ¢ θ∗ PF,t = ∗ Etηt Et−1 M Ct∗ Et1−ηt θ −1 h i Et = (17) (18) (19) (20) 1−ηt∗ θ Et−1 M Ct /Et ∗ PH,t = η∗ θ−1 Et t θ∗ PF∗,t = ∗ Et−1 (M Ct∗ ) θ −1 ² ³γ ² ∗ ³1−γ θ−1 θ −1 −η (1−γ) γW µt Et t ∗ θ θ Ct = ¡£1−γ γ¢ [Et−1 (M Ct )] Et−1 M Ct∗ Et1−ηt ² ³γ ² ∗ ³1−γ θ−1 θ −1 η∗ γ γW µ∗t Et t ∗ θ θ ° ±iγ Ct∗ = h ∗ 1−η Et−1 M Ct /Et t [Et−1 (M Ct∗ )]1−γ ² ³ 1−ηt∗ θ−1 M Ct M Ct /Et h i `t = γ + (1 − γ) 1−ηt∗ θκ Et−1 (M Ct ) Et−1 M Ct /Et # " ² ∗ ³ ∗ ∗ 1−ηt θ − 1 E M C M C t t ¢ t £ `∗t = (1 − γ) +γ θ∗ κ∗ Et−1 (M Ct∗ ) Et−1 M Ct∗ Et1−ηt 10 (21) (22) (23) (24) (25) (26) to (19) and (22), while import prices vary with the exchange rate, depending on the degree of exchange rate pass-through according to (20) and (21). Equilibrium consumption is determined in (23) and (24). Finally employment and output12 levels are determined according to (25) and (26). 3 Optimal exchange rate pass-through for given monetary policy What is the optimal degree of exchange rate pass-through onto export prices of Home goods in the Foreign market? Taking monetary stances and policy rules as given, Home firms choose η ∗ as to maximize (1). In a symmetric environment with p∗ (h) = PH∗ the first order condition is:13 £ ¢ ∗ θ κ Et−1 (αt Pt∗ Ct∗ ln Et ) /PH,t (27) 1= θ−1 Et−1 [ln Et ] Comparing (27) with (11), it follows that the optimal pass-through η ∗ is such that: i h ∗ ∗ ηt i h Et−1 αt µt Et ln Et η∗ Et−1 αt µ∗t Et t = (28) Et−1 [ln Et ] or, rearranging: Covt−1 h 1−η ∗ M Ct /Et t , ln Et i =0 (29) This is a key condition. At an optimum, the (reciprocal of the) markup in the export market must be uncorrelated with the (log of the) exchange rate. Trivially, if E is constant or fully anticipated, any degree of pass-through is consistent with the previous expression. But if E is not perfectly predictable, the optimal degree of pass-through will depend on the expected monetary 12 13 Recall that national outputs Yt and Yt∗ are respectively equal to `t /αt and `∗t /αt∗ . The optimal pass-through solves: h ∗ ¡θ ∗ 0 = Et−1 −κp̃t (h)−θ θ ln Et exp {ηt∗ θ ln Et } PH,t αt CH,t i ∗ ¡θ ∗ −Et p̃t (h)1−θ (1 − θ) ln Et exp {−ηt∗ (1 − θ) ln Et } PH,t CH,t /Pt Ct ∗ ∗ and equilibrium conditions imply: PH,t CH,t /γ = Pt∗ Ct∗ = Pt Ct /Et . 11 policies and the structure of the shocks.14 By the same token, the optimal pass-through chosen by Foreign firms selling in the Home market requires: ¡ (30) Covt−1 M Ct∗ Et1−ηt , ln (1/Et ) = 0. To build intuition, suppose that the Home marginal cost is uncorrelated with the exchange rate (this would be the case if Home monetary policy were deterministic and Foreign monetary policy did not respond to Home shocks). In this case the optimal pass-through chosen by Home firms is 100 percent: Home firms let their export prices absorb fluctuations of the exchange rate in order to avoid uncertainty of markup and profitability in the Foreign market. Suppose instead that domestic marginal costs move one to one with the exchange rate (this would be the case if there were no Home productivity shocks and Foreign monetary policy were deterministic). In this case the optimal pass-through for Home firms selling abroad is zero: maintaining export prices constant in Foreign currency is the best strategy to avoid fluctuations in export markups. Patterns of endogenous intermediate pass-through can emerge, as the following example illustrates. If the Home monetary authority adopted the −1 policy µt = (αt2 µ∗t ) , then it would be optimal for Home firms to choose ηt∗ = 0.5. Abroad, we would need M Ct∗ Et1−ηt to be uncorrelated with the exchange rate. This would be the case, for instance, if µ∗t = αt4 / (αt∗ )5 and ηt = 0.6. 4 Optimal monetary policy for given exchange rate pass-through Consider now the policymakers’ problem in a world Nash equilibrium where national monetary authorities are able to commit to preannounced rules, taking the pass-through coefficients as given.15 The problem faced by the Home 14 When monetary policy is exogenous (suboptimal) and firms are only allowed to choose between zero and 100 percent pass-through (that is, between local-currency and producercurrency pricing), the formula above is consistent with the analysis of Devereux and Engel [2001] and Bacchetta and van Wincoop [2001]. 15 For an analysis of optimal monetary behavior under discretion see Corsetti and Pesenti [2001 a]. 12 monetary authority is to maximize the indirect utility of the Home represen∗ ∞ ∗ ∗ tative consumer (1) with respect to {µt+τ }∞ τ =0 for given {µτ , ατ , ατ , ητ , ητ }τ =t . The Foreign authority faces a similar problem. Table 2 presents the closedform reaction functions, the solution to which is the global Nash equilibrium.16 To facilitate an intuitive understanding of the formulas, each reaction function is written in two ways: as a function of marginal costs and markups, or as a function of employment gaps and deviations from the law of one price. An optimal policy requires that the Home monetary stance be eased (µ increases) in response to a positive domestic productivity shock (α falls). Absent a policy reaction, a positive productivity shock would create both an output and an employment gap. In fact, ` would fall below (θ − 1) / (θκ). Actual output Y would not change, but potential output, defined as the equilibrium output the economy could reach if prices were fully flexible, would increase. In light of this, optimal monetary policy leans against the wind and moves to close the employment and output gaps. In general, however, the optimal response to a Home productivity shock will not close the output gap completely. Home stabilization policy, in fact, induces fluctuations in the exchange rate that add uncertainty to Foreign firms’ sales revenue from the Home market. For instance, a depreciation of the Home currency reduces the revenue of Foreign firms exporting to Home, as PF /E falls by a percentage 1 − η with the movement in the exchange rate. If Foreign marginal costs do not move in tandem with export sales revenue, Foreign firms’ profit margins shrink. Ex-ante, Foreign agents will require compensation for the additional risk they face in the Home market. They will therefore preset higher prices on their exports, lowering Home consumption on average. This is why the Home monetary adjustment required to close the domestic output gap is not optimal. Relative to such stance, domestic policymakers can improve utility by adopting a policy that equates, at the margin, the benefit from keeping domestic output close to its potential level with the loss 16 As well known, in this class of models optimal monetary rules such as the reaction functions of Table 2 do not provide a nominal anchor to pin down nominal expectations. The issue can be addressed by assuming that governments set national nominal anchors (such as target paths for PH and PF∗ ) and credibly threaten to tighten monetary policy if the price of domestic goods deviates from the target. Such threats, however, are never implemented in equilibrium. See e.g. Woodford [2002] and the Appendix of Corsetti and Pesenti [2001a]. 13 Table 2: Monetary authorities’ optimal reaction functions γ + (1 − γ) (1 − ηt ) γM Ct (1 − γ) (1 − ηt ) M Ct∗ Et1−ηt ¡ = + Et−1 (M Ct ) Et−1 M Ct∗ Et1−ηt θκ θ∗ κ∗ ∗ γ `t (1 − γ) (1 − ηt ) ∗ `t θ − 1 θ − 1 = + (31) PH,t PF,t γ + (1 − γ) γ + (1 − γ) ∗ ∗ Et PH,t Et PF,t 1−η ∗ 1 − γ + γ (1 − ηt∗ ) (1 − γ) M Ct∗ γ (1 − ηt∗ ) M Ct /Et t ° ± = + 1−η ∗ Et−1 (M Ct∗ ) Et−1 M Ct /Et t θκ θ∗ κ∗ ∗ ∗ ) γ (1 − η ` `t t t ∗−1 θ θ − 1 = ∗ + ∗ Et PF,t Et PH,t 1−γ+γ 1−γ+γ PF,t PH,t (1 − γ) from lower consumption (due to the effects of exchange rate volatility on the level of import prices). As long as η is below one, the Home monetary stance tightens when productivity worsens abroad and loosens otherwise. Rising costs abroad (an increase in α∗ ) lower the markup of Foreign goods sold at Home. If Home policymakers were not expected to stabilize the markup by raising rates and appreciating the exchange rate, Foreign firms would charge higher prices onto Home consumers. Only when η = 1 do Foreign firms realize that any attempt by the Home authorities to stabilize the markup is bound to fail as both PF and the exchange rate fall in the same proportion. 14 (32) With complete pass-through in both countries, the policies in a Nash equilibrium are: µt = Et−1 (αt µt ) αt µ∗t = Et−1 (αt∗ µ∗t ) αt∗ (33) Monetary authorities optimally stabilize marginal costs and markups. Output gaps are fully closed and employment remains unchanged at the potential level (θ − 1) / (θκ) or (θ∗ − 1) / (θ∗ κ∗ ). Both domestic and global consumption endogenously co-move with productivity shocks. Thus, the Nash optimal monetary policy supports the same allocation as would flexible prices. This result provides an extreme version of the case for flexible exchange rates made by Friedman [1953]: even without price flexibility, monetary authorities can engineer the right adjustment in relative prices through exchange rate movements. In our model with PCP, expenditure-switching effects makes exchange rate and price movements perfect substitutes. The Nash equilibrium will however not coincide with a flex-price equilibrium when the pass-though is less than perfect in either market. Consider for instance the case of LCP.17 In this case the optimal monetary policy in each country cannot be inward-looking, and must instead respond symmetrically to shocks anywhere in the world economy. The optimal monetary policy in Table 2 can in fact be written as: µ−1 ´ αt∗ αt + (1 − γ) (34) µt = γ Et−1 (αt µt ) Et−1 (αt∗ µt ) µ∗t ´ = γ αt αt∗ + (1 − γ) Et−1 (αt µ∗t ) Et−1 (αt∗ µ∗t ) µ−1 , (35) expressions that imply µ = µ∗ . In our model, the exchange rate is a function of the relative monetary stance µ/µ∗ . Our analysis then suggests that exchange rate volatility will be higher in a world economy close to purchasing power parity, and lower in a world economy where deviations from the law of one price are large. In fact, if the exposure of firms’ revenue to exchange rate fluctuations is limited, inward-looking policymakers assign high priority to stabilizing domestic 17 See the discussion in Devereux and Engel [2000]. 15 output and prices, with ‘benign neglect’ of exchange rate movements. Otherwise, policymakers ‘think globally’, taking into account the repercussions of exchange rate volatility on consumer prices; hence, the monetary stances in the world economy come to mimic each other, reducing currency volatility. The characterization of optimal monetary unions is a simple corollary of the analysis above. We define a monetary union µt = µ∗t as optimal if the single monetary stance µt is optimal for both countries. It is straightforward to show that when shocks are perfectly correlated, the optimal allocation is such that M Ct = Et−1 (M Ct ) and M Ct∗ = Et−1 (M Ct∗ ) regardless of the degree of pass-through. Optimal monetary policies support a fixed exchange rate regime and an optimal monetary union while fully closing the national output gaps. If shocks are asymmetric, a monetary union is optimal only when both countries find it optimal to choose a symmetric monetary stance, that is, when pass-through is zero worldwide. 5 Optimal exchange rate pass-through and monetary policy in equilibrium Recapitulating: Home and Foreign firms choose the levels of pass-through ηt∗ and ηt on the basis of their information at time t−1 regarding marginal costs and exchange rates at time t, by solving (29) and (30). Home and Foreign monetary authorities take the levels of pass-through ηt∗ and ηt as given and determine their optimal monetary stances by solving the conditions (31) and (32). We now consider the joint determination of µt , µ∗t , ηt and ηt∗ satisfying the four equations above in the non-trivial case in which the shocks αt and αt∗ are asymmetric. The following allocation is an equilibrium: M Ct = Et−1 (M Ct ) , M Ct∗ = Et−1 (M Ct∗ ) ηt = ηt∗ = 1 (36) Purchasing power parity holds and there is full pass-through of exchange rate changes into prices. Monetary policies fully stabilize the national economies by closing output and employment gaps. Exchange rates are highly volatile, their conditional variance being proportional to the volatility of αt∗ /αt . We will refer to this equilibrium as an optimal float (OF). 16 The logic underlying the OF case can be understood as follows. Suppose Foreign firms selling in the Home market choose η = 1 and let Home-currency prices of Foreign goods move one-to-one with the exchange rate, stabilizing their markups. Then the Home monetary authority chooses as a rule to stabilize Home output fully, no matter the consequences for the exchange rate (the volatility of which does not affect Foreign exporters’ profitability and therefore does not affect, on average, the price of Foreign goods paid by Home consumers). Note that when η = 1, Home output stabilization implies that M C is a constant. But this implies that the marginal costs of Home firms are uncorrelated with the exchange rate. Thus, Home firms will optimally set their pass-through abroad and choose η ∗ = 1 in order to stabilize the markup on their exports to the Foreign country. Since Home firms are now fully insulated from exchange rate fluctuations, the Foreign monetary authority optimally chooses to stabilize Foreign output with benign neglect of the exchange rate, so that M C ∗ is a constant. But in this case Foreign firms optimally choose η = 1 as we had assumed initially: the OF case is an equilibrium. Consider now the following allocation: M Ct∗ M Ct + (1 − γ) , Et−1 (M Ct ) Et−1 (M Ct∗ ) = ηt∗ = 0 1 = γ ηt Et = const (37) This is the LCP scenario brought to its extreme consequences: there is no pass-through of exchange rate changes into prices, but this hardly matters since the exchange rate is fixed! Optimal national monetary policies are fully symmetric, thus cannot insulate the national economies from asymmetric shocks: it is only on average that they stabilize the national economies by closing output and employment gaps — the most apparent case of an optimal currency area. To see why the previous scenario an equilibrium, note that if Home and Foreign firms choose η = η ∗ = 0, Home and Foreign authorities are concerned with the price-distortions of exchange rate volatility. They will optimize over the trade-off between employment stability and consumers’ purchasing power. While they choose their rules independently of each other, the rules they adopt are fully symmetric, thus leading to exchange rate stability. But if the exchange rate is constant, the choice of the pass-through is no longer 17 a concern for Home and Foreign firms: zero pass-through is as good as a choice as any other level of η and η ∗ . Such weak preference implies that the monetary union is an equilibrium. Would the two allocations above still be equilibrium allocation if national authorities could commit to coordinated policies, maximizing some weighted average of expected utility of the two national representative consumers? This is an important question, as one may argue that policymakers in a monetary union would set their rules together (taking private agents’ pricing and pass-through strategies as given), rather than independently. By the same token, if there were large gains from cooperation in a floating exchange rate regime, there would also be an incentive for policymakers to design the optimal float in a coordinated way. One may conjecture that, once cooperative policies are allowed for, the equilibrium allocation becomes unique. Remarkably, it turns out that the possibility of cooperation does not modify at all the conclusions of our analysis. It can be easily shown that optimal policy rules conditional on η, η ∗ = 1 are exactly the same in a Nash equilibrium and under coordination: there are no gains from cooperation in the PCP scenario which replicates the flex-price allocation.18 Also, as shown in Corsetti and Pesenti [2001a], optimal policy rules conditional on η, η ∗ = 0 are identical with and without cooperation: since exchange rate fluctuations are the only source of international spillover, there cannot be gains from cooperation when non-cooperative monetary rules already imply stable exchange rates!19 While there are policy spillovers for any intermediate degree of pass through (0 > η, η ∗ > 1), they disappear in equilibrium under the two extreme pass-through scenarios. In the only two cases relevant for our equilibrium analysis, optimal monetary policy rules are exactly the same whether or not the two national policymakers cooperate with each other. 18 See Obstfeld and Rogoff [2000a,b] and Corsetti and Pesenti [2001a]. With LCP, expected utility at Home is identical to expected utility in the Foreign country up to a constant that does not depend on monetary policy. For any given shock, consumption increases by the same percentage everywhere in the world economy. Even if ex-post labor moves asymmetrically (so that ex-post welfare is not identical in the two countries, as is the case under PCP), ex-ante the expected disutility from labor is the same as under flexible prices. 19 18 6 Endogenous OCAs: Macroeconomics and welfare analysis Can a monetary union be a self-validating OCA? Our model suggests that the answer is yes. Policy commitment to monetary union — i.e., the adoption of the rules (34-35) — leads profit-maximizing producers to modify their pricing strategies, lowering their pass-through elasticities. Such behavioral change makes a monetary union optimal, even if macroeconomic fundamentals and the pattern of shocks (αt and αt∗ in our framework) remain unchanged across regimes. A crucial result of our analysis is that, under an OCA, output correlation is higher than under the alternative OF equilibrium. In fact, under OF, monetary policies are such that employment in both countries is always stabilized (both ex-ante and ex-post) at the constant levels ` = (θ − 1) / (θκ) and `∗ = (θ∗ − 1) / (θ∗ κ∗ ). This implies that output correlation under OF depends on the degree of asymmetry of the fundamental shocks: ² ³ ² OF ∗OF ³ OF ∗OF ¡ `t 1 1 `t , , = Corr (38) = Corr Corr Yt , Yt αt αt∗ αt αt∗ Instead, in a monetary union, employment levels are functions of relative shocks: αt µOCA αt∗ µOCA θ∗ κ∗ ∗OCA θκ OCA t t = = `t , ` (39) ∗ OCA ∗−1 t θ−1 θ Et−1 (αt µOCA ) E (α ) t−1 t t µt where µOCA is the solution of the system (34)-(35). This implies that output levels are perfectly correlated: ² OCA ∗OCA ³ ¡ OCA ∗OCA ¡ ` ` = Corr t =1 , Yt , t ∗ , µOCA Corr Yt = Corr µOCA t t αt αt (40) OF ∗OF ¡ OCA ∗OCA ¡ , consistent with the tra≥ Corr Y , Y so that Corr Y ,Y ditional characterization of OCAs. It is possible to rank the OF and the OCA regimes in welfare terms. Focusing on the Home country, expected utility W in (1) can be written as: " À ¢ ∗ ∗ ηt 1−ηt £ !# ² ³ αt (µt ) µt E E (α µ ) t−1 t−1 t t f lex Wt−1 = Wt−1 − γEt−1 ln + (1 − γ) Et−1 ln t αt µt αt∗ (µ∗t )ηt µ1−η t (41) 19 where W f lex is independent of monetary regime, and equal to the utility that consumers could expect to achieve if prices were fully flexible. By Jensen’s inequality, the term in square brackets is always non-negative: expected utility with price rigidities is never above expected utility with flexible prices. At best, what monetary policy rules can do is to bridge the gap between the two. Observe that under the OF equilibrium (36) the term in square bracket becomes zero and W OF = W f lex . But this implies that W OF ≥ W OCA , an inequality that holds with strong sign when shocks are asymmetric. It follows that an optimal currency area is always Pareto-inferior vis-à-vis a Friedman-style optimal flexible exchange rate arrangement. 7 Discussion and conclusion The theory of optimal currency areas, from the classic contributions by Mundell [1961], McKinnon [1963], Kenen [1969] and Ingram [1973] to its modern applications and revisions,20 stresses that asymmetric, country-specific shocks represent a key element in the choice of exchange rate regime. Specifically, asymmetric real shocks weaken the case for a common currency, as member states of a monetary union lose their ability to use domestic exchange rate and interest rate policies for stabilization purposes. Conversely, business cycle synchronization and macroeconomic convergence make a currency area an optimal monetary arrangement, other things being equal, by reducing the scope for asymmetric policy responses to the disturbances hitting the union-wide economy. In terms of our model, an exogenous increase in the correlation of the real shocks leads to closer co-movements in optimal monetary stances for any level of exchange rate pass-through. The argument for an endogenous optimal currency area emphasizes that the monetary union itself could act as a catalyst of business cycle synchronization, essentially by reducing foreign exchange transaction costs and therefore by promoting trade integration across countries. Not everyone agrees with this argument: for instance Eichengreen [1992] and Krugman [1993] stress that monetary integration could lead to greater specialization in production, 20 Those include, among others, Eichengreen [1990, 1992], Dowd and Greenaway [1993], Tavlas [1993], Bayoumi and Eichengreen [1994], Melitz [1996] and Bayoumi [1997]. See Buiter, Corsetti and Pesenti [1998], ch.10, for a critical survey of the literature. 20 thus lowering output correlation and making regions more vulnerable to local shocks. On an empirical basis, however, the evidence presented by Frankel and Rose [1998] supports the view that trade links raise income correlations. The conclusion is that the OCA criterion may be satisfied ex-post even if it fails ex-ante. But what would happen if monetary integration fails to boost economic convergence and intra-industry trade? Would it still be possible for a monetary union to satisfy ex-post the OCA criterion when monetary and real integration fail to move in tandem? In this paper we have shown the existence of two equilibria in a standard open-economy model where the alternative between pricing-to-market and law of one price depends on endogenous choices by firms. This result suggests that credible policy commitment to monetary union may lead to a change in pricing strategies, making a monetary union the optimal monetary arrangement in a self-validating way. It is worth emphasizing that a common monetary policy is optimal because, for given producers’ pricing strategies, the use of the exchange rate for stabilization purposes would entail excessive welfare costs, in the form of higher import prices and lower purchasing power across countries. Once a monetary union takes off and firms adapt their pricing strategies to the new environment, the best course of action for the monetary authorities is to avoid any asymmetric policy response to asymmetric shocks. As a result, even in the absence of the structural effects of monetary integration stressed by Frankel and Rose [1997, 1998] (e.g., even without an increase in intra-industry trade), the correlation of national outputs increases. In sum, the best institutional device to guarantee a credible policy commitment to a monetary union is to have the monetary union itself in place. 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